The distance formula from a solid geometry line to a plane is d=(axbycz0?k)/√(a^2+b^2+c^2).

In solid geometry, the formula for the distance from a line to a plane can be derived based on the situation when the line is parallel to the plane. Assume that the parameters of the straight line L are a and b, the normal vector of the plane P is n, and the point (x0, y0, z0) is on the straight line.

At this time, the distance from the point (x0, y0, z0) to the plane ax+by+cz=k can be calculated by the formula: d=(axbycz0?k)/√(a^ 2+b^2+c^2), when the straight line is parallel to the plane, the distance from the line to the plane is equal to the distance from any point on the straight line to the plane. Therefore, the above formula can be used to calculate the shortest distance between the straight line L and the plane P.

It should be noted that the above formula only applies to the case where the straight line is parallel to the plane. If the line is not parallel to the plane, you will need to use other methods to calculate the distance from the line to the plane.

Problem-solving methods of solid geometry:

1. Definition method: Generally, the symmetry of graphics must be used, and oblique triangles must be solved during calculations. This method requires an in-depth understanding and mastery of the nature and characteristics of three-dimensional graphics.

2. Perpendicular line method: Generally, the perpendicular line of the plane is required to be easy to find, and a right triangle must be solved during calculation. This method is suitable for some vertical or oblique line problems and requires the use of mathematical knowledge such as trigonometric functions and the Pythagorean theorem.

3. Projective area method: Generally, there is only one common point between two intersecting surfaces, and this method is used when the intersection line of the two surfaces is not easy to find. This method requires understanding the projection rules of three-dimensional figures and solving three-dimensional geometry problems by finding the projected areas of two surfaces. In general, solving solid geometry problems requires the flexible use of various methods and techniques, while also focusing on the understanding and mastery of basic concepts and properties.